Author: Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 400
Book Description
Applied mechanics reviews
Author: Journal of the Society for Industrial and Applied Mathematics. Series B: Numerical Analysis
Author: Society for Industrial and Applied MathematicsPublisher:
ISBN:
Category : Numerical analysis
Languages : en
Pages : 944
Book Description
A Posteriori Error Estimation Techniques for Finite Element Methods
Author: Rüdiger VerfürthPublisher: Oxford University Press
ISBN: 0199679428
Category : Mathematics
Languages : en
Pages : 414
Book Description
A posteriori error estimation techniques are fundamental to the efficient numerical solution of PDEs arising in physical and technical applications. This book gives a unified approach to these techniques and guides graduate students, researchers, and practitioners towards understanding, applying and developing self-adaptive discretization methods.
Numerical Methods for Elliptic and Parabolic Partial Differential Equations
Author: Peter KnabnerPublisher: Springer Science & Business Media
ISBN: 038795449X
Category : Mathematics
Languages : en
Pages : 437
Book Description
This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.
Mathematical Aspects of Discontinuous Galerkin Methods
Author: Daniele Antonio Di PietroPublisher: Springer Science & Business Media
ISBN: 3642229808
Category : Mathematics
Languages : en
Pages : 392
Book Description
This book introduces the basic ideas to build discontinuous Galerkin methods and, at the same time, incorporates several recent mathematical developments. The presentation is to a large extent self-contained and is intended for graduate students and researchers in numerical analysis. The material covers a wide range of model problems, both steady and unsteady, elaborating from advection-reaction and diffusion problems up to the Navier-Stokes equations and Friedrichs' systems. Both finite element and finite volume viewpoints are exploited to convey the main ideas underlying the design of the approximation. The analysis is presented in a rigorous mathematical setting where discrete counterparts of the key properties of the continuous problem are identified. The framework encompasses fairly general meshes regarding element shapes and hanging nodes. Salient implementation issues are also addressed.
The Finite Element Method: Theory, Implementation, and Applications
Author: Mats G. LarsonPublisher: Springer Science & Business Media
ISBN: 3642332870
Category : Computers
Languages : en
Pages : 403
Book Description
This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.
Mathematical Reviews
Author: Certified Reduced Basis Methods for Parametrized Partial Differential Equations
Author: Jan S HesthavenPublisher: Springer
ISBN: 3319224700
Category : Mathematics
Languages : en
Pages : 139
Book Description
This book provides a thorough introduction to the mathematical and algorithmic aspects of certified reduced basis methods for parametrized partial differential equations. Central aspects ranging from model construction, error estimation and computational efficiency to empirical interpolation methods are discussed in detail for coercive problems. More advanced aspects associated with time-dependent problems, non-compliant and non-coercive problems and applications with geometric variation are also discussed as examples.
The Finite Element Method and Its Reliability
Author: Ivo BabuškaPublisher: Oxford University Press
ISBN: 9780198502760
Category : Mathematics
Languages : en
Pages : 820
Book Description
The finite element method is a numerical method widely used in engineering. Experience shows that unreliable computation can lead to very serious consequences. Hence reliability questions stand are at the forefront of engineering and theoretical interests. This book presents the mathematical theory of the finite element method and is the first to focus on the questions of how reliable computed results really are. It addresses among other topics the local behaviour, errors caused by pollution, superconvergence, and optimal meshes. Many computational examples illustrate the importance of the theoretical conclusions for practical computations. Graduate students, lecturers, and researchers in mathematics, engineering, and scientific computation will benefit from the clear structure of the book, and will find this a very useful reference.
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